Puzzle Test

Overview

Puzzle Test problems (also called analytical puzzles) are multi-step logical deduction questions where you must deduce facts about people, objects, or events from a series of clues. On CAT, these appear as 4–6 question DILR sets. On GMAT, they appear in lighter form in Data Sufficiency. The key is structured deduction — not guessing.

Common Puzzle Types

• Scheduling puzzles: Assign events to time slots or days. Clues restrict which events can be adjacent, which come before others, etc.
• Assignment puzzles: Match entities to attributes (person → city, color → house, etc.)
• Ranking/Comparison puzzles: Determine relative ordering (fastest, tallest, most expensive)
• Category puzzles: Each person belongs to exactly one category; deduce who belongs where

The Einstein Grid Method

For assignment puzzles, use a grid:

• Rows = one set of entities (people)
• Columns = another set (attributes: city, profession, pet, color, etc.)
• Each cell = matched or eliminated (✓ or ✗)

Rules:

• Each row has exactly one ✓ per attribute (bijection)
• When a cell is ✓, all other cells in the same row and column for that attribute become ✗
• Continue until all cells are determined

Reading Clues — Translation Table

Step-by-Step Approach

1. List all entities (people, objects, attributes) and their possible values
2. Extract definite facts (direct clues with no ambiguity) → mark in the grid immediately
3. Extract constraint clues (relative clues) → write them as inequalities or adjacency rules
4. Propagate: Once one cell is fixed, eliminate other options in the same row/column
5. Branch if necessary: When a clue allows 2 possible positions, try each — one will lead to contradiction

Scheduling Puzzles — Day/Time Assignment

Clues often specify:

• "X happens before Y" → X_day < Y_day
• "X and Y happen on consecutive days" → |X_day − Y_day| = 1
• "X does not happen on Monday"

Build a chain from ordering clues. Fix any entity with a unique valid position; propagate.

Common Mistakes

• Misreading "between" (two houses between A and B means positions differ by 3, not 2)
• Confusing "to the left of" (relative) with "on the leftmost" (absolute)
• In Einstein puzzles: marking a ✓ but forgetting to ✗ the rest of that row and column
• Assuming a constraint applies in both directions ("X is not next to Y" applies to both sides)

Exam Tips

• For CAT: draw the structure (row of houses, circular table, calendar grid) before reading clues
• Process clues in order of certainty: definite facts → small-range constraints → wide-range constraints
• When stuck: find the most constrained entity (fewest valid positions) and try each possibility
• Verify your final arrangement against ALL clues — not just the ones you used to build it
• In CAT sets, the 5–6 questions often test different aspects of the same puzzle — if your arrangement is wrong, multiple questions will be wrong simultaneously